Low-Rank wavelet solver for the Ornstein-Zernike integral equation

Maxim V. Fedorov, Heinz-Jürgen Flad, Lars Grasedyck, and Boris N. Khoromskij

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Submission date: 15. Jun. 2005
Pages: 24
published in: Computing, 80 (2007) 1, p. 47-73 
DOI number (of the published article): 10.1007/s00607-007-0221-7
Bibtex
with the following different title: A structured low-rank wavelet solver for the Ornstein-Zernike integral equation
MSC-Numbers: 65F50, 65F30, 46B28, 47A80
PACS-Numbers: 02.60.N, 61.20.Ne, 61.20.Gy
Keywords and phrases: wavelets, ornstein-zernike equation, simple fluids, data-sparse matrix approximations
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Abstract:
A structured wavelet algorithm is developed to solve the Ornstein-Zernike integral equation for simple liquids. The algorithm is based on the discrete wavelet transform of radial distribution functions and different low-rank matrix approximations. The fundamental properties of wavelet bases such as interpolation properties and orthogonality are employed to improve the convergence and speed of the algorithm. In order to solve the integral equation we have applied a combined scheme in which the coarse part of the solution is calculated by the use of wavelets in a multilevel method, while the fine part is solved by the direct iteration. Tests have indicated that the proposed procedure is more effective than the conventional method based on hybrid algorithms.